Finite Group Databasebeta

← #29580594

Subgroups — #29580594

Order 15616.

658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840090C211yesmaximal, characteristic, complemented
2C2×#16840073C211yesmaximal, characteristic
3C2×#16839499C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic
5#21444086C211yesmaximal, characteristic, complemented
6#21443662C211yesmaximal, characteristic, complemented
7C61×#2639C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9#16840090—22no—
10#16840090—22no—
11#16840073—22no—
12#16840073—22no—
13C2×#14519710—21no—
14C2×#14519708—21no—
15C2×#14519701—21no—
16C2×#14519698—21no—
17C2×C22⋊#92418C2211yescharacteristic
18C2×C22⋊#92418C2211yescharacteristic
19C2×#14519684—22no—
20C2×#14519684C2211yescharacteristic
21#16839499—22no—
22#16839496—22no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C61×#400—21no—
26C61×#397—21no—
27C61×#394—21no—
28C61×#393—21no—
29C61×#386—22no—
30C2×#95×C61C2211yescharacteristic
31C23×Dic61—21no—
32C23×Dic61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D412yes—
41#14519710—24no—
42#14519708—24no—
43#14519701—24no—
44#14519698—24no—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47C22⋊#92418D412yes—
48C22⋊#92418D412yes—
49#14519684—21no—
50#14519684—21no—
51#14519684—44no—
52C22×Q8×C61D411yescharacteristic
53C22×D4×C61—21no—
54C22×D4×C61D411yescharacteristic
55C23×C4×C61D412yes—
56C23×C4×C61C2311yescharacteristic
57C22⋊Q8×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61—21no—
60C22⋊Q8×C61—21no—
61#121×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72#95×C61—22no—
73#95×C61—22no—
74#95×C61—21no—
75#95×C61—21no—
76C24×C61—21no—
77C24×C61C2×D411yescharacteristic
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—42no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—42no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C22×C4×C61—22no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—41no—
106C22×Dic61—42no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—82no—
124C22⋊C4×C61—82no—
125C4⋊Dic61—22no—
126C4⋊Dic61—22no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C2×#92418—22no—
130C2×#92418—22no—
131C2×#92418—42no—
132C2×#92418—42no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—22no—
136C23×C61—41no—
137C23×C61—42no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—42no—
141C23×C61#12011yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12711yescharacteristic
144C23×C61#13512yes—
145C23×C61AGL(1,ℤ/8)12yes—
146Q8×C61—42no—
147Q8×C61—81no—
148D4×C61—42no—
149D4×C61—81no—
150D4×C61—82no—
151D4×C61—81no—
152D4×C61—81no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—44no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—82no—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×Dic61—44no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—44no—
179C2×Dic61—82no—
180C2×Dic61—81no—
181C2×Dic61—82no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184C2×Dic61—81no—
185#92418—42no—
186#92418—42no—
187#9971—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—82no—
197C22×C61—82no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#39211yescharacteristic
202C22×C61#44912yes—
203C22×C61#45511yescharacteristic
204C22×C61#45611yescharacteristic
205C22×C61#45812yes—
206C22×C61#46312yes—
207C22×C61#49511yescharacteristic
208C22×C61#49611yescharacteristic
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—82no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217Dic61—82no—
218Dic61—82no—
219C2×#483—611no—
220C2×#480—611no—
221#2639D6111yescharacteristic
222C2×#328—611no—
223C2×#327—611no—
224#1445—611no—
225#1280—611no—
226C2×C61—21no—
227C2×C61—22no—
228C2×C61—21no—
229C2×C61—161no—
230C2×C61#160912yes—
231C2×C61#161212yes—
232C2×C61#200711yescharacteristic
233C2×C61#201211yescharacteristic
234C2×C61#202211yescharacteristic
235C2×C22⋊Q8C2×D6111yescharacteristic
236C2×#121C2×D6111yescharacteristic
237C22×C4⋊C4—611no—
238#483—1222no—
239#483—1222no—
240#480—1222no—
241#480—1222no—
242C2×#107—1221no—
243C2×#106—1221no—
244C2×#103—1221no—
245C2×#102—1221no—
246C2×C22⋊C8—611no—
247C2×C22⋊C8—611no—
248#400—21no—
249#397—21no—
250#394—21no—
251#393—21no—
252#386—22no—
253C2×#95—611no—
254C2×#95—1222no—
255C2×#95C2×D6111yescharacteristic
256#328—1222no—
257#327—1222no—
258C61#997111yescharacteristic, complemented, Sylow
259C22×Q8C22⋊D6111yescharacteristic
260C22×D4—21no—
261C22×D4C22⋊D6111yescharacteristic
262C23×C4—1221no—
263C23×C4—1221no—
264C23×C4C22⋊D6112yes—
265C23×C4C22×D6111yescharacteristic
266C22×C8—1221no—
267C22×C8—1221no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—612no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4C22⋊D6111yescharacteristic
284C2×C4⋊C4C22⋊D6111yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289#107—1224no—
290#106—1224no—
291#103—1224no—
292#102—1224no—
293C22⋊C8—612no—
294C22⋊C8—612no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297#95—22no—
298#95—22no—
299#95—21no—
300#95—21no—
301#95—1221no—
302#95—1221no—
303#95—2444no—
304C24—21no—
305C24C2×C22⋊D6111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—1222no—
326C22×C4—1222no—
327C22×C4—2441no—
328C22×C4—2442no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2442no—
333C22×C4—2442no—
334C22×C4—2442no—
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4#1175822411yescharacteristic
339C22×C4C2×C22⋊D6111yescharacteristic
340C22×C4C2×C22⋊D6111yescharacteristic
341C2×C8—1222no—
342C2×C8—1222no—
343C2×C8—2442no—
344C2×C8—2442no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—1222no—
352C4⋊C4—1222no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C23—21no—
362C23—21no—
363C23—22no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—41no—
369C23#1451974611yescharacteristic
370C23#1451974811yescharacteristic
371C23#1451977311yescharacteristic
372C23#1451979712yes—
373C23#1451980212yes—
374Q8—42no—
375Q8—81no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—81no—
380D4—81no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—82no—
399C2×C4—4881no—
400C2×C4—4882no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4882no—
405C2×C4—2444no—
406C2×C4—2442no—
407C2×C4—2444no—
408C2×C4—2442no—
409C2×C4#1451974511yescharacteristic
410C2×C4#1451974511yescharacteristic
411C2×C4#1451974911yescharacteristic
412C2×C4#1451974911yescharacteristic
413C8—2442no—
414C8—2442no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—81no—
424C22—82no—
425C22—81no—
426C22—82no—
427C22—81no—
428C22#1683967011yescharacteristic
429C22#1683990712yes—
430C22#1683994011yescharacteristic
431C22#1683994511yescharacteristic
432C22#1683995212yes—
433C22#1683997412yes—
434C22#1684014411yescharacteristic
435C22#1684015211yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—82no—
443C4—81no—
444C4—4882no—
445C4—4882no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—161no—
450C2#2144481612yes—
451C2#2144483312yes—
452C2#2144686611yescharacteristic
453C2#2144689611yescharacteristic
454C2#2144694811yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2639C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenter#2639D61
hypocenterC61#9971
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2639

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840090C2semidirect
3. C2×#16839499C2semidirect
5. #21444086C2semidirect
6. #21443662C2semidirect
258. C61#9971semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168400902
C2×#168400732
C2×#168394992
C2×#168394962
#214440862
#214436622
C61×#26392
#997161